Branes and integrable lattice models

TL;DR

This paper reviews the connection between brane configurations in supersymmetric field theories and the construction of integrable lattice models, highlighting a novel approach using extended operators in topological quantum field theories.

Contribution

It introduces a new method to derive integrable lattice models from brane tilings and extended operators in topological quantum field theories.

Findings

Established a correspondence between brane tilings and integrable models

Demonstrated construction of lattice models from extended operators

Clarified the role of topological quantum field theories in this correspondence

Abstract

This is a brief review of my work on the correspondence between four-dimensional $\mathcal{N} = 1$ supersymmetric field theories realized by brane tilings and two-dimensional integrable lattice models. I explain how to construct integrable lattice models from extended operators in partially topological quantum field theories, and elucidate the correspondence as an application of this construction.